Determining stress in ferromagnetic materials from measurements of magnetic anisotropy and magnetic permeability

ABSTRACT

The absolute values of biaxial stresses in a ferromagnetic material (16) are measured using a probe (12) which comprises an electromagnet (26), a sensor (32) for stress-induced magnetic anisotropy (SMA) and a sensor (30) for directional effective permeability (DEP). The DEP sensor (30) enables absolute values of stress to be determined; the SMA sensor (32) enables the directions of the principal stress axes to be accurately determined, and improves the accuracy of the stress measurements.

This invention relates to a method and to an apparatus for measuringstress in a ferromagnetic material.

BACKGROUND OF THE INVENTION

Steel, which is a ferromagnetic material, is a widely used constructionmaterial. To evaluate the safety of a structure it would be desirablenot only to be able to detect defects (for example using ultrasonics),but also to measure the stress in the material, for example the stressaround a defect which affects the likely behaviour of the defect. Hencea reliable non-destructive way of measuring the total stress (includingresidual, applied, static and dynamic components) would be desirable. Avariety of magnetic techniques are known to have some sensitivity tostress, for example magnetoacoustic emission, Barkhausen emission,coercivity, stress-induced magnetic anisotropy, directional effectivepermeability, or incremental permeability over a whole magnetic cycle,although magnetic measurements are usually also affected by othermaterial properties such as microstructure. For example EP-A-0 389 877(Nikkoshi) teaches that stress in steel may be determined from thereversible magnetic permeability in the approach to saturation; it alsostates that using the variations in magnetic permeability to determineprincipal stresses does not enable reproducible results to be obtained.Ultrasonic measurements, X-ray diffraction and neutron diffraction canalso provide information about microstructure and/or stress. It has alsobeen suggested, for example in QT News, November 1992, that acombination of magnetic techniques may enable the effects of residualstress to be isolated.

According to the present invention there is provided a method formeasuring stress in a ferromagnetic material, the method using a probecomprising an electromagnet means defining an electromagnet core and twospaced apart electromagnet poles, a first magnetic sensor between thetwo poles and arranged to sense magnetic flux density perpendicular tothe direction of the free space magnetic field between the poles, asecond magnetic sensor arranged to sense the reluctance of that part ofthe magnetic circuit between the poles of the electromagnet means, andmeans to generate an alternating magnetic field in the electromagnetmeans, the method comprising arranging the probe with the poles adjacentto a location on a surface of the ferromagnetic material, generating analternating magnetic field in the electromagnet means and so also in theferromagnetic material with a maximum amplitude well below magneticsaturation, turning the probe so the alternating magnetic field in theferromagnetic material has in succession a plurality of differentorientations, detecting the signals from the first sensor with themagnetic field in the plurality of different orientations, determiningfrom the orientations of the magnetic field at which the maxima andminima of the signals from the first sensor occur the directions of theprincipal stress axes, detecting the signals from the second sensor atleast when the magnetic field is aligned with the directions of theprincipal stress axes, processing the signals from the second magneticsensor by backing them off with a back-off signal preset such that whenthe probe is adjacent to a stress-free location the backed-off signal iszero, and then resolving that component of the backed-off signal which,in the impedance plane, is perpendicular to the effect of lift-off fromthe surface, and using the values of the resolved component with themagnetic field aligned with the directions of the principal stress axesto determine the values of the principal stresses at that location inthe material.

The first sensor would detect no signal if the material were exactlyisotropic; however stress induces anisotropy into the magneticproperties of the material, and so the signals received by the firstsensor are a measure of this stress-induced magnetic anisotropy (SMA).The variations in the SMA signal as the probe is rotated enable thedirections of the principal stress axes to be accurately determined. Thefirst sensor is preferably a first sensing coil, and the measured signalmay be the emf induced in the first sensing coil. The use of a magneticmeasurement of this type is described in WO 89/01613 (Langman).

The second sensor senses the reluctance of that part of the magneticcircuit between the poles and so it provides a measure of thepermeability of the material through which the flux passes. As the probeis turned this sensor hence provides a signal indicative of theeffective permeability of the material in different directions: this isreferred to as directional effective permeability (DEP). The secondsensor is preferably a second sensing coil, and is preferably wound ontothe electromagnet core. In this case the signals from the coil relate tothe reluctance of the complete magnetic circuit. The measured parametermight be the impedance of the coil. The alternating magnetic field ispreferably generated by a coil, which may be the second sensing coil,but is preferably a separate coil as this enables a better signal tonoise ratio to be achieved, and in this case the measured parameter ispreferably the induced emf. Alternatively the second sensor might bearranged between the poles, to detect the magnetic flux density parallelto the free space magnetic field; the flux density in this casedecreases as the permeability increases. The DEP signals enable thevalues of the stress to be determined; this determination requires theSMA signals in order to specify the stress axes accurately, and mayutilise the SMA signals too in determining the values of the principalstresses.

Thus, before DEP measurements are made, the probe is placed adjacent toa region of surface where the stress is negligible (or at any rateknown) and the value of the signal is then backed off to give zerosignal. The small changes in DEP due to stress are then easier tomeasure.

The DEP signals can be resolved as a component in-phase with the currentcreating the alternating field, and a component in quadrature to that;these components correspond to resistance and reactance in the impedanceplane. If the gap between the surface and the probe (the lift-off)varies, this has an effect on the DEP signals. This change correspondsto a direction in the impedance plane oriented in a direction referredto as the lift-off angle. Hence to avoid spurious effects due to changesin lift-off, the output DEP signal is then resolved in a direction atright angles to the lift-off direction in the impedance plane. Both theback-off and the lift-off initialisation must be performed beforemeasurements can be made.

The electromagnet means may comprise a C or U-shaped core of laminatedtransformer steel (e.g. grain oriented silicon steel). Other materialscan be adopted as long as they have good magnetic permeability andsufficiently high magnetic saturation, such as mu-metal. A coil of wireis wound around the core and is connected to a suitable alternatingcurrent supply. As indicated earlier this coil may be used as the secondsensor, as its impedance varies with the permeability of the materialunder test. Better sensitivity can be achieved however by winding twocoils on the core, one of which is connected to the current supply andthe other acts as the second sensor; this arrangement provides a bettersignal to noise ratio. In operation the magnetizing field due to thecurrent alternates, driving the material under test through smallhysteresis loops with a maximum amplitude (typically a few A/cm) wellbelow magnetic saturation. The operating frequency is desirably between50 Hz and 1000 Hz, most preferably between 100 Hz and 500 Hz. The lowerthe frequency the greater the effective depth of penetration of themagnetic changes below the surface.

The size of the probe is desirably small; for example it might fitwithin a cylindrical casing of external diameter less than 50 mm,preferably less than 20 mm. This makes possible good spatial resolution(as the magnetic properties are effectively averaged over the area ofthe end of the probe adjacent to the two poles). Furthermore the smallerthe probe diameter the less is the effect of any curvature of thesurface of the material.

The SMA and DEP measurements may be made simultaneously. Alternativelythey may be made successively, and in this case they may be made withdifferent frequencies of alternating current (and so of magnetic field),for example at 300 Hz for DEP and at 68 Hz for SMA. Preferably theamplitudes of the alternating currents are such that the magnetic fieldhas the same value for both SMA and DEP measurements. Ideally themeasurements would both be made at the same frequency, to achieve thesame depth of penetration. However DEP is more sensitive to stress athigher frequencies, so in practice the frequency at which DEP isperformed is a compromise between sensitivity and penetration. Indeedthe frequency may be varied in order to vary the depth of penetration.

The probe may be turned through a complete revolution, and measurementsof both SMA and DEP made continuously or at several angularorientations, for example every 10°. The rotation may be performedmanually, or by a motor; and the probe preferably incorporates a sensorto provide signals representing its orientation. The SMA measurementsvary approximately sinusoidally with angular orientation of the probe,with maxima and minima when the magnetic field direction in the materialis aligned with the bisector of the angle between the principal stressaxes in the plane tangential to the surface. Determination of the probeorientations for which the SMA measurements have their maxima and minimatherefore enables the directions of the principal stress axes to bedetermined.

DEP measurements are also required with the magnetic field direction(i.e. the line joining the centre of the two poles) oriented with theprincipal stress axes, at which orientations the DEP measurements havetheir maxima and minima. Preferably DEP measurements are made at severaldifferent orientations, and on the basis of the known way in which DEPvaries with orientation all the measurements can be used to obtain amore accurate estimate of the values at the principal stress axes.

The probe of the invention enables stresses, including residualstresses, in a steel structure to be measured non-destructively, atleast in a region near the surface of the structure. The probe can bescanned over the surface to find how the stresses vary with position,for example in the vicinity of a weld. The probe can readily be adaptedfor underwater use, for example by a diver for inspecting under-seaparts of an oil rig.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will now be further described by way of example only, andwith reference to the accompanying drawings in which:

FIG. 1 shows a diagrammatic view of an apparatus for measuring stress;

FIG. 2 shows a longitudinal sectional view of a probe for use in theapparatus of FIG. 1;

FIG. 3 shows graphically the variations in SMA and DEP signals measuredduring rotation of the probe of FIG. 2;

FIG. 4 shows graphically experimental measurements of the variation ofthe DEP signal with biaxial stresses, with the probe aligned parallel toa principal stress axis;

FIG. 5 shows graphically experimental measurements of the variation ofthe DEP signal with biaxial stresses, with the probe aligned parallel tothe other principal stress axis; and

FIG. 6 shows graphically experimental measurements of the variation ofthe SMA signal with biaxial stresses

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring to FIG. 1, a stress measuring apparatus 10 includes a sensorprobe 12 comprising SMA (stress-induced magnetic anisotropy) and DEP(directional effective permeability) sensors, the probe 12 beingattached to an electric motor 14 which can be held by an operator, orwhich may be held by a support mechanism (not shown), so the motor 14can turn the probe 12 with one end adjacent to a surface of a steelobject 16 in which the stress is to be determined. The sensor probe 12and motor 14 are connected by a 2 m long umbilical cable 17 to a signalconditioning/probe driver unit 18. The unit 18 is itself connected by along umbilical cable 19 (which may be for example up to 300 m long) toan interface unit within a microcomputer 20, which has a keyboard 21.Operation of the apparatus 10 is controlled by software in themicrocomputer 20.

The interface unit within the microcomputer 20 generates sine and cosinefunctions at an angular frequency selectable by software, and buffersthe sine waveform for transmission to the unit 18 for driving the probe12. The amplitude of the transmitted waveform is also selectable bysoftware. It also provides control signals to control the angularposition of the probe 12 by means of the motor 14. The interface unitalso provides control signals to the unit 18 to select which of thesignals available from the probe 12 is to be transmitted for analysis.It demodulates the selected input signal (SMA or DEP) to derive itsin-phase and quadrature components, filters the demodulated signal toremove high frequency components and to reduce noise, and converts theanalogue signals to digital form for input to the computer 20. It alsodetects the angular position of the probe 12 from signals from aposition encoder (not shown) on the motor 14.

The long umbilical cable 19 incorporates a coaxial cable to transmit theselected signal (SMA or DEP), and wires to control which signal isselected, to control the motor 14, to transmit signals from the positionencoder, to transmit the sinusoidal waveform, and to convey electricalpower. The unit 18 converts the drive waveform from a voltage to acurrent drive for the probe 12; buffers and amplifies the SMA and DEPsignals from the probe; and selects which signal is to be transmitted tothe microcomputer 20. It also buffers the signals from the positionencoder for transmission, and drives the motor 14 in response to controlsignals.

Referring now to FIG. 2 the probe 12 is shown detached from the motor14, in longitudinal section though with the internal components shown inelevation. The probe 12 comprises a cylindrical brass casing 24 ofexternal diameter 16.5 mm and of overall height 60 mm, the upper halfbeing of reduced diameter whereby the probe 12 is attached to the motor14. The upper half of the casing 24 encloses a head amplifier 25. Thelower half encloses a U-core 26 of laminated mu-metal (a highpermeability nickel/iron/copper alloy) whose poles 28 are separated by agap 7.5 mm wide, and are each of width 2.3 mm, and of thickness 10 mm(out of the plane of the Figure). The poles 28 are in the plane of thelower end of the casing 24. Around the upper end of the U-core 26 is aformer on which are wound two superimposed coils 30. One coil 30 (whichhas 200 turns) is supplied with the sinusoidal drive current from theunit 18; the other coil 30 (which has 70 turns) provides DEP signals.Between the two poles 28 is a rectangular resin-impregnated paperlaminate former on which is wound a 1670-turn rectangular coil 32, about4 mm high and 6 mm wide, and 6 mm-square as seen from below, thewindings lying parallel to the plane of the Figure so the longitudinalaxis of the coil 32 is perpendicular to the line between the centres ofthe poles 28. The coil 32 is supported by a support plate 34 fixedbetween the arms of the U-core 26 so the lower face of the coil 32 is inthe plane of the poles 28. The coil 32 provides the SMA signals. Boththe DEP and the SMA signals are amplified by the head amplifier 25before transmission to the unit 18.

In operation of the system 10 the motor 14 is supported so the lower endof the probe 12 is adjacent to the surface of the object 16 and thelongitudinal axis of the probe 12 is normal to the surface. The probe 12is first placed adjacent to a region of the object 16 where the stressesare negligible. An alternating current of the desired frequency andamplitude is supplied to the drive coil 30. The in-phase and quadratureDEP signals received by the microcomputer 20 are firstly backed off tozero and the backing off value then fixed; then the probe 12 is liftedslightly, and from the changes in the DEP signals the lift-off angle inthe impedance plane is determined.

The probe 12 is then placed adjacent to a region in which the stress isto be measured. The orientation of the line joining the centres of thepoles 28 (referred to as the orientation of the probe 12) is notedrelative to a fixed direction on the surface. The motor 14 is thenenergised to turn the probe 12, for example in a step-wise fashion 10°at a time through a total angle of 380°. At each orientation of theprobe 12 the quadrature SMA signal is measured (at a drive currentfrequency of 68 Hz), and the DEP signal in a direction in the impedanceplane perpendicular to the lift-off direction is determined (at a drivecurrent such as to produce the same magnetic field but at a frequency of300 Hz). The current is typically in the range 300 to 400 mA.

Referring to FIG. 3 there are shown graphically the values of thequadrature SMA signals, and of the DEP signals (backed-off and resolvedat right angles to the lift-off angle) at different orientations of theprobe 12, indicated as the angle from the initial orientation, asexperimentally determined on a steel specimen. It will be observed thatthe SMA values vary sinusoidally with probe orientation and that theorientation for which the SMA values have their maxima and minima canreadily be determined. The directions midway between these twoorientations are the directions of the principal stress axes. The DEPvalues are less accurate (the vertical lines through the plotted pointsindicating the uncertainty in the measurements), but as they should varysinusoidally with probe orientation the values of DEP in the principalstress directions can hence be determined.

The values of the stresses in the directions of the principal stressaxes can then be determined from the experimental measurements of DEP inthose directions, and from the magnitude of the fluctuations in the SMAsignal during rotation of the probe 12. This requires calibration of theapparatus 10, taking measurements in the manner described above on asample of material of the same type as that of the object 16, whilesubjecting it to a variety of different stresses. This may be done witha cross-shaped sample, whose arms are aligned with the axes of a testrig, SMA and DEP measurements being made at the centre of the samplewhere the principal stress directions are aligned with the axes of thetest rig.

Referring now to FIGS. 4 and 5, these indicate by contours the measuredvalues of DEP. FIG. 4 shows the DEP values on the principal stress axisclosest to the x-axis of the sample; FIG. 5 shows the DEP values on theprincipal stress axis closest to the y-axis of the sample. The valueswere obtained with a steel plate subjected to a wide range of tensileand compressive stresses parallel to the x and y axes of the sample.Referring to FIG. 6, this indicates similarly the measured values of thedifference between the maximum and minimum of the quadrature SMA signalduring rotation of the probe 12, for the same range of stresses appliedto the same steel sample.

Ideally it would be possible to determine the biaxial stresses in theobject 16 from measured values of just two of these parameters, byconsidering where the corresponding contours intersect in the stressplane. However there is in practice some uncertainty in the measuredvalues, and also in the calibration measurements. A more accurateassessment of the biaxial stress in the object 16 can be made asfollows. For each position in the stress plane the total number ofstandard deviations between the measured value of a parameter and thevalue obtained during calibration is calculated (taking into account thestandard errors in both the parameter and in the calibration map). Theregions in the stress plane where this quantity is small will be similarto the appropriate contour, but the width of the region is quantified interms of the number of standard deviations from a perfect fit. Thiscalculation is performed for two, and preferably all three measuredparameters (as in FIGS. 4, 5 and 6), and the mean number of standarddeviations for all the parameters is calculated for each position in thestress plane. The value of the biaxial stress in the object 16 is thentaken to be the centroid of the region in the stress plane for which themean number of standard deviations is less than, for example, two. Anestimate of the uncertainty in this value of biaxial stress is given bythe mean number of standard deviations at that position in the stressplane.

It will be appreciated that the apparatus of the invention may differfrom that described above. For example the SMA signal might be sensed bya Hall effect sensor, or by a magneto-resistor, rather than a sensorcoil. The motor to turn the probe 12 might be beside rather than at thetop end of the probe 12. The probe might also incorporate additionalsensors, for example a magnetic sensor to sense the magnetic fluxdensity between the poles parallel to the free-space field direction.The head amplifier 25 might be located within the unit 18 instead ofbeing in the probe 12. It will also be appreciated that the frequenciesof the alternating drive currents might be different from thosedescribed, and that the manner in which the signals are interpretedmight differ from that described. Some of these alternatives will now bedescribed in more detail.

It will be appreciated that, with the probe 12, the DEP measurements areobtained by sensing the magnetic flux density in the core 26, whichincreases as the permeability of the test object 16 increases.Alternatively the DEP measurements might be obtained using an air-coredcoil (not shown), between the arms of the U-core 26, whose longitudinalaxis is parallel to the free-space field direction. Such a coil detectsleakage flux, which will decrease as the permeability of the test object16 increases. If such a coil is close to the plane of the poles 28 itprovides signals which are affected very little by lift-off, but areaffected by stress. If such a coil is remote from the poles 28, forexample above the support plate 34, it is affected by lift-off to asimilar extent to a coil close to the plane of the poles 28, but hasalmost no sensitivity to stress in the test object 16. Hence analternative probe utilises two such coils, one close to the plane of thepoles 28 and one remote from the poles 28. The signals are subtractedfrom each other, so that much of the noise is eliminated and littlebacking-off of the resultant signal is required; to minimize therequired backing off the upper coil may have fewer turns than the oneclose to the plane of the poles. Such a probe may have greatersensitivity to stress and a better signal-to-noise ratio than the probe12, but is more complex.

In the probe 12, no attempt was made to correct the SMA signals forlift-off. This may be achieved by providing an air-cored reference coil40 between the arms of the U-core 26 and above the support plate 34, thelongitudinal axis of the coil 40 being parallel to the free-space fielddirection, as described above. By monitoring the signal from thisreference coil 40 during SMA measurement, the magnitude of the SMAsignals can be simply corrected for lift-off. This requires acalibration of the signal from this coil 40 and the attenuation of theSMA signal with lift-off, and experimental measurements have shown thatthese are related linearly. For example the reference coil 40 might be200 turns of copper wire on a rectangular former. The signals from sucha reference coil 40 can also be used to normalise the SMA and DEPsignals for any variations in gain, magnetic field strength, orfrequency.

As described earlier, calibration of the apparatus 10 may be done bymaking many measurements on a cross-shaped sample of the material ofwhich the object 16 is made when subjected to a wide range of differentbiaxial stresses. Alternatively the apparatus may be calibrated using asimple bar-shaped sample subjected to four or five different uniaxialstresses, and combining such calibration measurements with a parametricmodel of the variation of SMA and DEP to biaxial stresses. Hence thestresses within the object 16 can be determined. This method ofcalibration provides the benefits of requiring a simpler sample ofmaterial, requiring far fewer calibration measurements, and with simplerstresses.

Whatever method of calibration is adopted the results will be misleadingif the crystal structure of the object 16 has changed, for example withformation of martensite which is both mechanically and magneticallyharder than ferrite. The permeability is consequently lower, as are theDEP measurements, so the calculated values of stress would be lower thanthe true values. The presence of such microstructural changes can bedetected by measuring the coercivity of the object 16. This may be doneusing the drive coil 30 and measuring the signals obtained from the DEPcoil.

One procedure is to apply a low frequency (e.g. 0.05 Hz) current to thedrive coil 30, of large peak current (e.g. 1.5 A), so the region of theobject 16 adjacent to the probe 12 is driven to saturation in alternatedirections. The signal emf from the DEP coil has a peak value whichoccurs every half-cycle, and the value of the drive current at whichthis occurs (or, more accurately, the mean of the magnitudes of the twovalues of drive current at which this occurs in a complete cycle) isdirectly proportional to the coercivity.

We claim:
 1. A method for measuring stress in a ferromagnetic material,the method using a probe (12) comprising an electromagnet means definingan electromagnet core (26) and two spaced apart electromagnet poles(28), a first magnetic sensor (32) between the two poles (28) andarranged to sense magnetic flux density perpendicular to the directionof the free space magnetic field between the poles (28), a secondmagnetic sensor (30) arranged to sense the reluctance of that part ofthe magnetic circuit between the poles (28) of the electromagnet means,and means (30) to generate an alternating magnetic field in theelectromagnet means, the method comprising arranging the probe (12) withthe poles (28) adjacent to a location on a surface of a ferromagneticmaterial (16), generating an alternating magnetic field in theelectromagnet means and so also in the ferromagnetic material (16) witha maximum amplitude well below magnetic saturation, turning the probe(12) so the alternating magnetic field in the ferromagnetic material(16) has in succession a plurality of different orientations, detectingthe signals from the first sensor (32) with the magnetic field in theplurality of different orientations, determining from the orientationsof the magnetic field at which the maxima and minima of the signals fromthe first sensor (32) occur the directions of the principal stress axes,detecting the signals from the second sensor (30) at least when themagnetic field is aligned with the directions of the principal stressaxes, processing the signals from the second magnetic sensor (30) bybacking them off with a back-off signal preset such that when the probeis adjacent to a stress-free location the backed-off signal is zero, andthen resolving that component of the backed-off signal which, in theimpedance plane, is perpendicular to the effect of lift-off from thesurface, and using the values of the resolved component with themagnetic field aligned with the directions of the principal stress axesto determine the values of the principal stresses at that location inthe material (16).
 2. A method as claimed in claim 1 wherein the signalsfrom the first and the second sensors (32, 30) are obtainedsimultaneously.
 3. A method as claimed in claim 1 wherein the signalsfrom the first and the second sensors (32, 30) are obtainedsuccessively.
 4. A method as claimed in claim 3 wherein the magneticfield is generated at a different frequency when obtaining signals fromthe first sensor (32) than when obtaining signals from the second sensor(30).
 5. A method as claimed in claim 2 wherein the frequency at whichthe magnetic field is generated is varied to vary the penetration depthof the measurements.
 6. A method as claimed in claim 1 wherein thesignals from the first sensor (32) are also used in the determination ofthe values of the principal stresses.
 7. A method as claimed in claim 1wherein the signals from the second sensor (30) are detected at theplurality of different orientations, and the values of the resolvedcomponent at all the orientations are used to determine the values ofthe resolved component with the magnetic field aligned with thedirections of the principal stress axes.
 8. An apparatus suitable foruse in a method for measuring stress in a ferromagnetic material, theapparatus comprising a probe (12) comprising an electromagnet meansdefining an electromagnet core (26) and two spaced apart electromagnetpoles (28), a first magnetic sensor (32) between the poles (28) andarranged to sense magnetic flux density perpendicular to the directionof the free-space magnetic field between the poles (28), a secondmagnetic sensor (30) arranged to sense the reluctance of that part ofthe magnetic circuit between the poles (28) of the electromagnet means,and means (30) to generate an alternating magnetic field in theelectromagnet means, and the apparatus also comprising means to provideoutput signals representing the flux density sensed by the firstmagnetic sensor (32), and signals representing the reluctance sensed bythe second magnetic sensor (30), and means to process the reluctancesignals by backing them off with a back-off signal preset such that whenthe probe is adjacent to a stress-free location the backed-off signal iszero, and then resolving that component of the backed-off signal which,in the impedance plane, is perpendicular to the effect of lift-off fromthe surface of the material to provide second output signals.
 9. Anapparatus as claimed in claim 8 also comprising a third magnetic sensorarranged to sense the magnetic flux density parallel to the direction ofthe free space magnetic field, between the arms but spaced away from thepoles (28).
 10. An apparatus as claimed in claim 8 also comprising means(14) to rotate the probe to a plurality of different orientations.